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a(n) = floor(A344875(n) / A011772(n)).
5

%I #9 Jun 20 2021 19:19:14

%S 1,1,1,1,1,2,1,1,1,3,1,1,1,2,1,1,1,3,1,1,2,2,1,2,1,3,1,6,1,1,1,1,1,3,

%T 1,7,1,2,2,4,1,1,1,2,3,2,1,1,1,3,1,2,1,2,4,1,2,3,1,3,1,2,1,1,1,5,1,7,

%U 1,3,1,1,1,3,2,2,2,6,1,1,1,3,1,1,1,2,1,4,1,2,5,6,2,2,3,2,1,3,1,7,1,1,1,2,3

%N a(n) = floor(A344875(n) / A011772(n)).

%H Antti Karttunen, <a href="/A344972/b344972.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = (A344875(n)-A344973(n)) / A011772(n) = floor(A344875(n) / A011772(n)).

%F a(n) = floor(A344971(n) / A344970(n)). - _Antti Karttunen_, Jun 20 2021

%o (PARI)

%o A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772

%o A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };

%o A344972(n) = floor(A344875(n)/A011772(n));

%Y Cf. A011772, A344875, A344876, A344969, A344970, A344971, A344973.

%K nonn

%O 1,6

%A _Antti Karttunen_, Jun 04 2021